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  • Open Access

Projective measurements: Topological quantum computing with an arbitrary number of qubits

Themba Hodge, Philipp Frey, and Stephan Rachel*

  • *Contact author: stephan.rachel@unimelb.edu.au
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APS Open Sci. 1, 000074 – Published 29 July, 2026

DOI: https://doi.org/10.1103/5q9d-3dc7

Abstract

Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a critical yet often overlooked challenge arises when scaling beyond two qubits: the naive extension of braiding-based gates fails to support even the full Clifford group. To overcome this limitation, we incorporate projective measurements that enable transitions between different qubit encodings, thus restoring computational universality. We perform many-body simulations of braiding dynamics augmented with measurement-based switching, explicitly preparing the Bell state and Greenberger–Horne–Zeilinger state for systems of two and five qubits, respectively. Furthermore, we execute a random unitary circuit on five qubits, achieving a fidelity exceeding 99%. We analyze the circuit's robustness by studying its fidelity dependence on total braid duration and static potential disorder. Our results show that the fidelity remains above 99% for moderate disorder, underscoring the intrinsic fault tolerance of the architecture. Finally, we demonstrate a random circuit on a ten-qubit system to showcase the scalability of our techniques.

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APS Open Sci. 1, 000074– Published 29 July, 2026
Vol. 1
  • Received 19 August 2025
  • Accepted 14 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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